PHYS212
: Lectures
Next:
Contents
Up:
PHYS212
PHYS212 : Classical and Quantum Mechanical Waves : Lectures
Lewis A. Riley
Copyright © 2003-2009
Contents
1. From Mechanical Oscillations to Waves
1.1 Complex Numbers and Complex Exponentials
1.2 Simple Harmonic Oscillations
1.2.1 The Differential Equation and its Solutions
1.2.2 Mass and Spring
1.2.3 Physical Pendulum
1.3 Two Coupled Oscillators
1.3.1 Double Pendulum
1.3.2 Beads on a String : Transverse Modes
1.4 Many Coupled Oscillators
1.4.1 Beads on a String
1.4.2 Compound Pendulum or Hanging Chain
1.5 The Continuous Limit : Waves on a String
1.5.1 The Equation of Motion : The Wave Equation
1.5.2 Solutions : Plane Waves
1.5.3 Normal Modes : Standing Waves
2. Wave Packets
2.1 Periodic and Confined Packets
2.1.1 Beats
2.1.2 Fourier Series
2.1.3 A Square Wave
2.2 Localized Packets
2.2.1 An alternative Fourier Series
2.2.2 Fourier Transformations
2.2.3 A Square Pulse
2.2.4 A Square Wave Packet
2.2.5 A Gaussian Pulse
2.3 Fourier Analysis in Frequency and Time
2.3.1 Fourier Series, Take II
2.3.2 A Square Wave
2.3.3 Fourier Transformations, Take II
2.3.4 A Square Pulse
2.4 Bandwidth Limits
3. Waves in Inhomogeneous Media
3.1 The Hanging Cable
3.1.1 The Equation of Motion
3.1.2 The Solutions : Bessel Functions of Order Zero
3.2 The WKB Approximation
3.2.1 The Method
3.2.2 Limit of Validity
3.2.3 Standing Waves on an Inhomogeneous String
4. Acoustic Waves
4.1 The Wave Equation
4.1.1 Displacement Waves
4.1.2 Pressure Waves
4.1.3 The Speed of Sound in an Ideal Gas
4.2 Energy, Power, and Intensity
4.2.1 Energy Density
4.2.2 Intensity
4.2.3 Decibels
4.3 Reflection, Refraction, and Transmission
4.3.1 Plane Waves in Three Dimensions
4.3.2 Planar Boundaries
4.4 The Doppler Effect
4.4.1 Moving Source
4.4.2 Moving Observer
4.4.3 Moving Source and Observer
4.5 Appendix : Adiabatic Expansion of an Ideal Gas
4.5.1 Specific Heats and the Gas Constant
4.5.2 Adiabatic Expansion
4.5.3 About
5. Electromagnetic Waves
5.1 The Wave Equation
5.2 Plane Waves
5.3 Polarization
5.4 Energy, Power, and Intensity
5.4.1 Energy Density
5.4.2 Intensity and the Poynting Vector
5.4.3 Radiation Pressure
5.5 Reflection, Refraction, and Transmission
5.6 The Doppler Effect
6. Diffraction
6.1 Double Slit, Take I
6.2 Single Slit
6.3 Double Slit, Take II
7. Quantum Mechanical Waves
7.1 Wavefunctions and Probability
7.2 The Schrödinger Equation
7.2.1 Separation of Variables
7.2.2 Plane Waves
7.2.3 Aside : Convenient Units
7.2.4 Standing Waves : The Infinite Square Well
7.3 Continuity and Probability Current
7.3.1 Defined
7.3.2 Plane Waves
7.3.3 Infinite Square Wells
7.4 Free Particles
7.4.1 Potential Steps
7.4.2 Square Barriers and Tunneling
7.4.3 Potential Ramps and the WKB Approximation
7.4.4 Gaussian Wave Packets
7.5 Bound Particles
7.5.1 A Packet in a Box
7.5.2 Finite Square Well Review
7.5.3 The Quantum Harmonic Oscillator
7.5.4 WKB Thinking : Qualitative Sketches
7.6 Time Dependent Perturbation Theory
7.6.1 The Coupled Equations
7.6.2 First Order Corrections
7.6.3 Second Order Corrections
7.7 Transitions and Radiation
7.7.1 Electric Dipole (E1) Transitions
7.7.2 Selection Rules
7.7.3 Spontaneous Emission and Lifetimes
7.7.4 E1 Transitions of an Electron Oscillator
A. Animations
Getting the Animations
Running the Animations
About this document ...
Next:
Contents
Up:
PHYS212
Copyright © 2003-2009, Lewis A. Riley
Updated Wed Jan 18 09:51:28 2006
